Reflection filter

ABSTRACT

A method and apparatus for generating a reflection filter. The method comprises the steps of determining an averaged step response of an acquired signal and generating a spectrum response from the averaged step response. A time at which a reflection in the averaged step response begins is determined and information in the averaged step response after the determined time when the reflection begins is replaced with an ideal flat line response to generate a required step response. A spectrum response is generated from the required step response and each frequency point of the spectrum response corresponding to the required step response is divided by each frequency point of the spectrum response corresponding to the averaged step response to generate a spectrum of the reflection filter. The result of the dividing step is processed to generate a reflection filter impulse response.

BACKGROUND OF THE INVENTION

Electronic signals are acted upon by transmission through varioussystems, conduits or the like. These conduits have various inherentphysical properties, one of them being impedance. This impedance is thetotal opposition to the flow of current offered by a circuit. Atransmission line that is terminated with a load impedance equal to thecharacteristic impedance Z_(o) of the line will not reflect an incidentwave at that point, and the transmission line is said to be impedancematched. However, a transmission line that is terminated with a loadimpedance different than Z_(o) will reflect part of an incident waveback toward the source or generator of the signal.

Reflections are often undesirable and should be eliminated. This isbecause at any point along the transmission line, that value of thesignal will appear as a combination of the originally transmittedsignal, and the reflected signal, thus resulting in distortion of theoriginally transmitted signal. Indeed, the voltage seen at anyparticular point on the line will be the vector sum of the transmittedand reflected sinusoids. Because the phase between the transmitted andreflected signals varies with position along the signal line, the vectorsums at different points along the transmission paths will be different,thus affecting the actual signal present on the transmission line, andat the output thereof.

SUMMARY OF THE INVENTION

In accordance with the present invention, the reflections created in asignal when there is a change in the impedance of the signal path areused advantageously. When a high or low impedance is encountered in thesignal path, a portion of the signal is reflected back in proportion tothe impedance change. By obtaining the time at which reflection occurson the signal, the impedance mismatch location can be pinpointed in thecircuit. Once the location is known, in accordance with the invention, apredetermined algorithm is employed to generate a filter that isdesigned to offset any effects generated by the reflected signal.Filtering such a received signal with a Reflection Filter constructed inaccordance with the invention removes the reflected waveform in thesampled signal without significantly effecting the rise time orovershoot of the signal.

Thus, a user is able to receive an output signal without any noisegenerated by the reflected signal, even when signal path geometry makesit impossible to precisely impedance match all components along thepath.

Still other objects and advantages of the invention will in part beobvious and will in part be apparent from the specification and thedrawings.

The invention accordingly comprises the several steps and the relationof one or more of such steps with respect to each of the others, and theapparatus embodying features of construction, combination(s) of elementsand arrangement of parts that are adapted to effect such steps, all asexemplified in the following detailed disclosure, and the scope of theinvention will be indicated in the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the invention, reference is made tothe following description and accompanying drawings, in which:

FIG. 1 is a frequency spectrum response of an information signal;

FIG. 2 is a step response of an information signal from which thefrequency spectrum response of FIG. 1 was generated;

FIG. 3 is an required step response of an information signal that wouldresult if a reflected signal were removed;

FIG. 4 is a frequency response spectrum of the required step response ofFIG. 3;

FIG. 5 is a frequency response spectrum of an required response filterbased upon the spectrums of FIGS. 4 and 1;

FIG. 6 is an impulse response of the frequency response spectrum of FIG.5;

FIG. 7 is a reflection filter comprising a windowed and truncatedversion of the impulse response of FIG. 6;

FIG. 8 is a frequency response of the impulse response of FIG. 7;

FIG. 9 is a filtered version of the step response information signal ofFIG. 2 employing the reflection filter frequency response of FIG. 8; and

FIG. 10 is a flow chart depicting reflection building processing inaccordance with one embodiment of the invention

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention is preferably implemented in an oscilloscope, thusallowing for the filtering of signals that are to be tested and viewedon the oscilloscope. However, the invention is not so limited, and maybe implemented, in part or in whole, on any electronic instrument thatwould find benefit from removing the effects of a reflected signal froma signal transmission path.

Referring next to the figures, a first embodiment of the invention willnow be described. FIG. 10 is a flowchart showing the overall processingof the reflection filter building process in accordance with theinvention. As is shown in FIG. 10, at step 1010, a step responseincluding a reflected signal is obtained. Such a signal is shown in FIG.2, which depicts an Averaged Step response from the system having areflection. A multiple number of step responses are acquired with thesame system settings and trigger position. These responses at each pointfor the different step responses are added and then divided by the totalnumber of acquisitions to give the Averaged Step response. Thisprocedure is shown in equation 1, which depicts the averaging of M stepresponses, each having N sample points

$\begin{matrix}{{{y_{{Avg}.{original}_{step}}\lbrack i\rbrack} = {\frac{1}{M} \times {\sum\limits_{j = 1}^{M}{y_{j}\lbrack i\rbrack}}}}{i = {{0\mspace{14mu}\ldots\mspace{14mu} N} - 1}}} & \left. 1 \right)\end{matrix}$For nomenclature, we further define x as being equal to the averagedoriginal as follows in equation 2.x_(original) _(step) =y_(Avg.original) _(step)   2)

When performing this acquisition and averaging procedure, it isimportant that the system settings and the trigger position do notchange between acquisitions; otherwise the averaging may give incorrectresults. The averaged Step response can be sampled at any sample rate.If the sample rate of the eventual required reflection filter isdifferent than the sample rate of the Averaged Step, interpolation ordecimation will be employed to have the Averaged Step response samplerate equal the sample rate at which the reflection filter is to beapplied. The averaging procedure noted above is performed on the sampledwaveform to reduce random noise in the signal, which changes fromacquisition to acquisition. This allows the user to view systemcharacteristics in the signal more clearly. Instead of averaging thestep signal it is also possible to obtain the step containing thereflection signal by using the averaged spectrum and then convertingthat information in time domain using Fourier transform.

Referring back to FIG. 10, processing passes to step 1020. In step 1020,once the Averaged Step response has been obtained, it is examined todetermine at what time the reflection begins. An ideal step responsewould have a value of zero until the stepped input occurs. Immediatelyupon receipt of the step input, the value will be one. Step responsesfrom actual physical systems are typically far from the ideal stepresponse. The imperfections in the actual responses are a result of manyfactors, some of which include bandwidth limitations and less than idealroll-off of the frequency response of practical systems. Theseimperfections manifest themselves as overshoot and ringing in the stepresponses, for example. Overshoot and ringing, though not present in theideal step response, should not be considered to have been generated bya signal reflection in the system. As noted above, reflection is causedby a change of impedance in the signal path. Overshoot and ringing, onthe other hand, are caused by bandwidth limitations and roll-off of thesystem. If the source of reflection in the signal path, i.e. theimpedance change in the circuit path, generates a reflection of thesignal that appears at the output of the system too close in time to thestep input, it is likely that the effects of the reflected signal on theoutput signal will combine with the overshoot and ringing effects on theoutput signal, thus making it very difficult to perform only reflectioncorrection without affecting the overshoot and ringing effects of thesignal. Therefore, preferably a first impedance mismatch in the signalpath is located far enough away from the output of the system so that areflection start point is able to be chosen at a location in the outputsignal that is after the ringing and overshoot responses of the signalhave settled down. By close examination of the example signal depictedin FIG. 2, it is determined that the reflection in the example signalstarts at approximately 400 ps after the rising edge.

In order to remove the effects of the detected reflection from thesignal, first an required reflection removed signal is constructed atstep 1025 of FIG. 10. This is the required response that wouldpreferably be obtained if there were no impedance mismatch, andtherefore nor reflection, in the signal. Constructing such an requiredresponse is performed by first determining a time at which reflectionstarts in the original waveform, as noted above. After this time hasbeen determined, the information in the data signal resulting from thereflection is replaced by an ideal flat line response, as is shown inFIG. 3. This required step response therefore mimics a response thatwould ideally be generated if there were no reflection in the system.This required system response is used as a reference response forgenerating a reflection filter in accordance with the invention.

This required response is determined in accordance with the followingequations 3-. In equation 3, startIndex is set to be the designatedpoint from which the reflection signal is believed to start, asdetermined above. The required step response is therefore definedequations 3 and 4 as follows:x_(required) _(step) [i]=x_(original) _(step) [i] for i=0 . . .startIndex−1 and  3)x_(required) _(step) [i]=P for i=startIndex . . . N−1where P is a constant determined by averaging the values occurring afterthe startIndex of the original step response so as to determine thevalue that should be applied to the replacement straight line in FIG. 3,as shown in equation 5.

$\begin{matrix}{P = {\frac{1}{N - {startIndex}} \times {\sum\limits_{j = {startIndex}}^{N - 1}{x_{{original}_{step}}\lbrack j\rbrack}}}} & \left. 5 \right)\end{matrix}$

Next, this required step response of FIG. 3 is differentiated inaccordance with equation 6, resulting in a corresponding requiredimpulse response shown at step 1030 of FIG. 10.x _(required) _(impulse) [i]=x _(required) _(step) [i+1]x _(required)_(step) [i] i=0 . . . N−2.  6)To ensure that the impulse response is the same size as the stepresponse, the last value of the impulse response is repeated, as shownin equation 7:x _(required) _(impulse) [N−1]=x _(required) _(impulse) [N−2]  7)

The DFT of this required impulse response is in turn taken in accordancewith equation 8, resulting in a spectrum corresponding to the requiredstep response at step 1040.

$\begin{matrix}{{X_{{required}_{spectrum}}\lbrack k\rbrack} = {{\sum\limits_{n = 0}^{N - 1}{{{x_{{required}_{step}}\lbrack n\rbrack} \cdot \;{\mathbb{e}}^{\frac{{- {j2\pi}}\;{kn}}{N}}}\mspace{14mu} k}} = {{0\mspace{14mu}\ldots\mspace{14mu} N} - 1}}} & \left. 8 \right)\end{matrix}$FIG. 4 shows this spectrum, and represents the required reflectionremoved spectrum.

During processing of the required spectrum in accordance with steps1020, 1025, 1030 and 1040 (or at another convenient time), a spectrum ofthe step response shown in FIG. 2 is obtained by first differentiatingthe step response points of FIG. 2 at step 1045 to generate an impulseresponse of the step response of FIG. 2. This differentiation is shownin equation 9:x _(original) _(impulse) [i]=x _(original) _(step) [i+1]−x _(original)_(step) [i] i=0 . . . N−2  9)As with the required response, to ensure that the impulse response isthe same size as the step response, we repeat the last value of theimpulse response, as shown in equation 10:x _(original) _(impulse) [N−1]=x _(original) _(impulse) [N−2]  10)

Thereafter, at step 1048, the DFT of the generated impulse response istaken in accordance with equation 11, resulting in the spectrum of thesystem for which the step response of FIG. 2 was obtained.

$\begin{matrix}{{X_{{original}_{spectrum}}\lbrack k\rbrack} = {{\sum\limits_{n = 0}^{N - 1}{{{x_{{original}_{step}}\lbrack n\rbrack} \cdot \;{\mathbb{e}}^{\frac{{- {j2\pi}}\;{kn}}{N}}}\mspace{14mu} k}} = {{0\mspace{14mu}\ldots\mspace{14mu} N} - 1}}} & \left. 11 \right)\end{matrix}$FIG. 1 depicts this resulting spectrum of the system of which the stepresponse signal of FIG. 2 was obtained. As is evident from FIG. 1, someripple is present in the frequency spectrum. This ripple is caused bythe reflection detected in the step response.

As is further evident from the spectrum of the required step response ofFIG. 4, the ripples in the spectrum depiction of FIG. 1 that were causedby the reflection are no longer present. Thus, in the spectrum of FIG. 4obtained from the required step response of FIG. 4, the effects of thereflection have been removed. A smooth spectrum is generated.

After generation of the spectrum of the required step response and thespectrum of the original step response signal, the spectrum of a desiredraw reflection filter (FIG. 5) is obtained by dividing each frequencypoint of the spectrum of the required step response by the correspondingpoints of the frequency response obtained of the step response includingthe reflection at step 1050. This process is shown in equation 12:

$\begin{matrix}{{{X_{{Raw}\text{-}{reflectionFilter}_{spectrum}}\lbrack k\rbrack} = \frac{X_{{required}_{spectrum}}\lbrack k\rbrack}{X_{{original}_{spectrum}}\lbrack k\rbrack}}{k = {{0\mspace{14mu}\ldots\mspace{14mu} N} - 1}}} & \left. 12 \right)\end{matrix}$The spectrums have both magnitude and phase information in the complexdata. Both magnitude and phase are considered while generating thereflection filter to ensure similar overshoot and ringing effects in theeventual filtered system as were present in the original responsewithout filtering. The reflection filter only effects the originalsignal after the previously determined starting time of the reflection.

Processing next proceeds to step 1060, where the impulse response of thespectrum of the desired raw reflection filter of FIG. 5 is generated bytaking the inverse Fourier Transform thereof, resulting in the impulseresponse shown in FIG. 6. This inverse Fourier Transform is generated inaccordance with equation 13:

$\begin{matrix}{{{x_{{Raw}\text{-}{reflectionFilter}_{impulse}}\lbrack n\rbrack} = {\frac{1}{N}{\sum\limits_{k = 0}^{N - 1}{{X_{{Raw}\text{-}{reflectionFilter}_{spectrum}}\lbrack k\rbrack} \cdot {\mathbb{e}}^{\frac{{j2\pi}\;{kn}}{N}}}}}}{n = {{0\mspace{14mu}\ldots\mspace{14mu} N} - 1}}} & \left. 13 \right)\end{matrix}$This inverse Fourier Transform of the spectrum of FIG. 5 generates rawreflection filter taps. This reflection filter is considered “raw”because some processing of the filter is still required before use, suchas like windowing and truncation of the generated taps.

This impulse response is then windowed and truncated in step 1070,resulting in a smaller length reflection filter. To perform thiswindowing and truncating, the impulse response is first multiplied witha Hanning window, in this preferred embodiment. The Hanning window isgenerated in accordance with equation 14:

$\begin{matrix}{{w_{hanning}\lbrack i\rbrack} = {{0.5 - {{0.5 \cdot {\cos\left( \frac{2{\pi\left( {i + N} \right)}}{2N} \right)}}\mspace{14mu} i}} = {{0\mspace{14mu}\ldots\mspace{14mu} N} - 1}}} & \left. 14 \right)\end{matrix}$Windowing of the impulse response is performed to reduce any spectralleakage of the frequency response. This windowing is performed bymultiplying the Hanning window with the raw reflection filter impulseresponse to generate a windowed impulse response in accordance withequation 15:x _(windowedreflection) _(impulse) [n] x _(Raw-reflectionFilter)_(impulse) [n]·w _(hanning) [n] n=0 . . . N−1  15)The windowed impulse response is then truncated, and the generatedpoints are used as the reflection filter coefficients. The response istruncated to remove all points which are too small in value (usuallybelow a predetermined threshold value) to make any significant change inthe frequency response of the reflection filter. The threshold value isselected such that when the value of the windowed reflection impulseresponse becomes less than the predetermined threshold value theremaining portion of the impulse response is truncated. By removingthese values, a smaller number of coefficients are required in thefilter, making the filter more efficient. This truncation procedure isshown in equation 16:x_(ReflectionFilterTaps)[n]=x_(windowedreflection) _(impulse) [n] n=0 .. . K−1  16)

-   -   where K<=N and abs(x_(windowedreflection) _(impulse)        [n])>Threshold Value    -   for all n=0 . . . K−1

This truncated filter is the final reflection filter generated inaccordance with the invention, and is shown in FIG. 7. This finalreflection filter is preferably implemented as a Finite Impulse Response(FIR) filter, employed to remove the reflection from any signal input tothe system. The frequency response of the filter resulting from thewindowed and truncated impulse response is generated at step 1090, andis shown in FIG. 8.

During operation, and in order to verify the success of the filterbuilding algorithm, a step signal (such as that shown in FIG. 2, andrepresented at step 1075) with reflection is passed through thegenerated filter. The resulting output signal at step 1080, and as shownin FIG. 9, is displayed as a step response with the system reflectionremoved. The removal of this reflection has no visible effect onovershoot or rise time of the signal. The reflection filter has acted onand removed only the reflection signal from the originally acquiredsignal.

While the invention has primarily been described with respect to amethod for performing the steps of the invention, it should beunderstood that the invention is also intended to include variousprocessing platforms, such as oscilloscopes, that will implement suchprocessing. As is known in the art, these processing apparatuses includeat least acquisition modules, memory, processors, displays and outputmodules. Therefore such a processing apparatus, as well as softwareintended to run on these apparatuses to implement the above describedmethod is considered to be part of the invention.

It will thus be seen that the objects set forth above, among those madeapparent from the preceding description, are efficiently attained and,because certain changes may be made in carrying out the above method andin the construction(s) set forth without departing from the spirit andscope of the invention, it is intended that all matter contained in theabove description and shown in the accompanying drawings shall beinterpreted as illustrative and not in a limiting sense.

It is also to be understood that the following claims are intended tocover all of the generic and specific features of the invention hereindescribed and all statements of the scope of the invention which, as amatter of language, might be said to fall therebetween.

1. A method for generating a reflection filter, comprising the steps of:determining a step response of an acquired signal; generating a spectrumresponse from the determined step response; determining a time at whicha reflection in the determined step response begins; replacinginformation in the determined step response after the determined timewhen the reflection begins with an ideal flat line response to generatea required step response; generating a spectrum response from therequired step response; dividing each frequency point of the spectrumresponse corresponding to the required step response by each frequencypoint of the spectrum response corresponding to the determined stepresponse to generate a spectrum of the reflection filter; and processingthe result of the dividing step to generate a reflection filter impulseresponse.
 2. The method of claim 1, further comprising the steps of:windowing the reflection filter impulse response; and truncating thereflection filter impulse response.
 3. The method of claim 2, whereinthe windowing is performed by multiplying a Hanning window with thereflection filter impulse response.
 4. The method of claim 2, whereinone or more points generated upon truncating of the reflection filterimpulse response are used as the reflection filter coefficients.
 5. Themethod of claim 1, wherein the reflection filter impulse response isimplemented as a Finite Impulse Response (FIR) filter.
 6. The method ofclaim 1, wherein the spectrum response is generated from the determinedstep response by: differentiating the determined step response togenerate an impulse response of the determined step response; anddetermining a Discrete Fourier Transform (DFT) of the impulse responseof the determined step response.
 7. The method of claim 1, wherein thespectrum response is generated from the required step response by:differentiating the required step response to generate an impulseresponse of the required step response; and determining a DiscreteFourier Transform (DFT) of the impulse response of the required stepresponse.
 8. The method of claim 1, wherein the time at which areflection in the determined step response begins is determined to be ata time after any effects on the signal due to ringing and overshoot havesubstantially settled.
 9. The method of claim 1, wherein the processingof the result of the dividing step to generate a reflection filterimpulse response comprises performing an inverse Fourier Transform onthe result of the dividing step.
 10. The method of claim 1, wherein thedetermined step response is an average of a number of acquired stepresponses derived from said signal.
 11. A method for generating areflection filter, comprising the steps of: measuring a predeterminednumber of step responses; averaging the measured step responses togenerate an averaged step response of the measured step responses;determining a time at which a reflection in the averaged step responsebegins; replacing information in the averaged step response after thedetermined time when the reflection begins with an ideal flat lineresponse to generate a required step response; differentiating therequired step response to generate an impulse response of the requiredstep response; determining a Discrete Fourier Transform (DFT) of theimpulse response of the required step response to generate a spectrumresponse from the required step response; differentiating the averagedstep response to generate an impulse response of the averaged stepresponse; determining a Discrete Fourier Transform (DFT) of the impulseresponse of the averaged step response to generate a spectrum responsefrom the averaged step response; dividing each frequency point of thespectrum response corresponding to the required step response by eachfrequency point of the spectrum response corresponding to the averagedstep response to generate a spectrum of the reflection filter;performing an inverse Fourier Transform on the result of the dividingstep to generate a reflection filter impulse response; windowing thereflection filter impulse response; and truncating the reflection filterimpulse response.
 12. A method for generating a reflection filter foruse in an oscilloscope, comprising the steps of: acquiring a waveformhaving a step response by the oscilloscope; determining a step responseof the acquired waveform; generating a spectrum response from thedetermined step response; determining a time at which a reflection inthe determined step response begins; replacing information in thedetermined step response after the determined time when the reflectionbegins with an ideal flat line response to generate a required stepresponse; generating a spectrum response from the required stepresponse; dividing each frequency point of the spectrum responsecorresponding to the required step response by each frequency point ofthe spectrum response corresponding to the determined step response togenerate a spectrum of the reflection filter; and processing the resultof the dividing step to generate a reflection filter impulse responsefor implementation in the oscilloscope.
 13. The method of claim 12,wherein the determined step response is an average of a number ofacquired step responses derived from said waveform.
 14. A processingapparatus for generating a reflection filter, comprising: means fordetermining a step response of an acquired signal; means for generatinga spectrum response from the determined step response; means fordetermining a time at which a reflection in the determined step responsebegins; means for replacing information in the determined step responseafter the determined time when the reflection begins with an ideal flatline response to generate a required step response; means for generatinga spectrum response from the required step response; means for dividingeach frequency point of the spectrum response corresponding to therequired step response by each frequency point of the spectrum responsecorresponding to the determined step response to generate a spectrum ofthe reflection filter; and means for processing the result from thedividing means to generate a reflection filter impulse response.
 15. Theapparatus of claim 14, further comprising: means for windowing thereflection filter impulse response; and means for truncating thereflection filter impulse response.
 16. The apparatus of claim 15,wherein the means for windowing performs the windowing by multiplying aHanning window with the reflection filter impulse response.
 17. Theapparatus of claim 15, wherein one or more points generated upontruncating of the reflection filter impulse response are used as thereflection filter coefficients.
 18. The apparatus of claim 14, whereinthe reflection filter impulse response is implemented as a FiniteImpulse Response (FIR) filter.
 19. The apparatus of claim 14, whereinthe means for generating a spectrum response from the determined stepresponse further comprises: means for differentiating the determinedstep response to generate an impulse response of the determined stepresponse; and means for determining a Discrete Fourier Transform (DFT)of the impulse response of the determined step response.
 20. Theapparatus of claim 14, wherein the means for generating a spectrumresponse from the required step response further comprises: means fordifferentiating the required step response to generate an impulseresponse of the required step response; and means for determining aDiscrete Fourier Transform (DFT) of the impulse response of the requiredstep response.
 21. The apparatus of claim 14, wherein the means fordetermining a time at which a reflection in the determined step responsebegins determines the time at which the reflection in the determinedstep response begins to be at a time after any effects on the signal dueto ringing and overshoot have substantially settled.
 22. The apparatusof claim 14, wherein the means for processing the result from thedividing means to generate a reflection filter impulse response performsan inverse Fourier Transform on the result from the dividing means. 23.The apparatus of claim 14, wherein the determined step response is anaverage of a number of acquired step responses derived from said signal.24. An apparatus for generating a reflection filter, comprising: meansfor measuring a predetermined number of step responses; means foraveraging the measured step responses to generate an averaged stepresponse of the measured step responses; means for determining a time atwhich a reflection in the averaged step response begins; means forreplacing information in the averaged step response after the determinedtime when the reflection begins with an ideal flat line response togenerate a required step response; means for differentiating therequired step response to generate an impulse response of the requiredstep response; means for determining a Discrete Fourier Transform (DFT)of the impulse response of the required step response to generate aspectrum response from the required step response; means fordifferentiating the averaged step response to generate an impulseresponse of the averaged step response; means for determining a DiscreteFourier Transform (DFT) of the impulse response of the averaged stepresponse to generate a spectrum response from the averaged stepresponse; means for dividing each frequency point of the spectrumresponse corresponding to the required step response by each frequencypoint of the spectrum response corresponding to the averaged stepresponse to generate a spectrum of the reflection filter; means forperforming an inverse Fourier Transform on the generated spectrum of thereflection filter to generate a reflection filter impulse response;means for windowing the reflection filter impulse response; and meansfor truncating the reflection filter impulse response.
 25. An apparatusfor generating a reflection filter, comprising: a processor, theprocessor performing the steps of: determining a step response of anacquired signal; generating a spectrum response from the determined stepresponse; determining a time at which a reflection in the determinedstep response begins; replacing information in the determined stepresponse after the determined time when the reflection begins with anideal flat line response to generate a required step response;generating a spectrum response from the required step response; dividingeach frequency point of the spectrum response corresponding to therequired step response by each frequency point of the spectrum responsecorresponding to the determined step response to generate a spectrum ofthe reflection filter; and processing the result of the dividing step togenerate a reflection filter impulse response.
 26. The apparatus ofclaim 25, wherein the processor further performs the steps of: windowingthe reflection filter impulse response; and truncating the reflectionfilter impulse response.
 27. The apparatus of claim 26, wherein theprocessor further performs the step of multiplying a Hanning window withthe reflection filter impulse response to perform the windowing.
 28. Theapparatus of claim 26, wherein the processor uses one or more pointsgenerated upon truncating of the reflection filter impulse response asthe reflection filter coefficients.
 29. The apparatus of claim 25,wherein the processor further implements the reflection filter impulseresponse as a Finite Impulse Response (FIR) filter.
 30. The apparatus ofclaim 25, wherein the processor, to generate the spectrum response fromthe determined step response, further performs the steps of:differentiating the determined step response to generate an impulseresponse of the determined step response; and determining a DiscreteFourier Transform (DFT) of the impulse response of the determined stepresponse.
 31. The apparatus of claim 25, wherein the processor, togenerate the spectrum response from the required step response, furtherperforms the steps of: differentiating the required step response togenerate an impulse response of the required step response; anddetermining a Discrete Fourier Transform (DFT) of the impulse responseof the required step response.
 32. The apparatus of claim 25, whereinthe processor determines the time at which a reflection in thedetermined step response begins to be at a time after any effects on thesignal due to ringing and overshoot have substantially settled.
 33. Theapparatus of claim 25, wherein the processor performs an inverse FourierTransform on the result of the dividing step in order to process theresult of the dividing step to generate a reflection filter impulseresponse.
 34. The apparatus of claim 25, wherein the determined stepresponse is an average of a number of acquired step responses derivedfrom said signal.
 35. An oscilloscope for generating a reflectionfilter, comprising: a processor, the processor performing the steps of:acquiring a waveform having a step response by the oscilloscope;determining a step response of the acquired waveform; generating aspectrum response from the determined step response; determining a timeat which a reflection in the determined step response begins; replacinginformation in the determined step response after the determined timewhen the reflection begins with an ideal flat line response to generatea required step response; generating a spectrum response from therequired step response; dividing each frequency point of the spectrumresponse corresponding to the required step response by each frequencypoint of the spectrum response corresponding to the determined stepresponse to generate a spectrum of the reflection filter; and processingthe result of the dividing step to generate a reflection filter impulseresponse for implementation in the oscilloscope.
 36. The oscilloscope ofclaim 35, wherein the determined step response is an average of a numberof acquired step responses derived from said waveform.
 37. A computerprogram embodied in a computer-readable medium to control a processingapparatus, the computer program including instructions to perform thesteps of: determining a step response of an acquired signal; generatinga spectrum response from the determined step response; determining atime at which a reflection in the determined step response begins;replacing information in the determined step response after thedetermined time when the reflection begins with an ideal flat lineresponse to generate a required step response; generating a spectrumresponse from the required step response; dividing each frequency pointof the spectrum response corresponding to the required step response byeach frequency point of the spectrum response corresponding to thedetermined step response to generate a spectrum of the reflectionfilter; and processing the result of the dividing step to generate areflection filter impulse response.
 38. The computer program of claim37, further comprising instructions for: windowing the reflection filterimpulse response; and truncating the reflection filter impulse response.39. The computer program of claim 38, further comprising an instructionfor multiplying a Hanning window with the reflection filter impulseresponse to perform the windowing.
 40. The computer program of claim 38,further comprising an instruction for using one or more points generatedupon truncating of the reflection filter impulse response as thereflection filter coefficients.
 41. The computer program of claim 37,further comprising an instruction for implementing the reflection filterimpulse response as a Finite Impulse Response (FIR) filter.
 42. Thecomputer program of claim 37, further comprising instructions forgenerating the spectrum response from the determined step response by:differentiating the determined step response to generate an impulseresponse of the determined step response; and determining a DiscreteFourier Transform (DFT) of the impulse response of the determined stepresponse.
 43. The computer program of claim 37, further comprisinginstructions for generating the spectrum response from the required stepresponse by: differentiating the required step response to generate animpulse response of the required step response; and determining aDiscrete Fourier Transform (DFT) of the impulse response of the requiredstep response.
 44. The computer program of claim 37, further comprisingan instruction for determining the time at which a reflection in thedetermined step response begins to be at a time after any effects on thesignal due to ringing and overshoot have substantially settled.
 45. Thecomputer program of claim 37, further comprising an instruction forprocessing the result of the dividing step to generate a reflectionfilter impulse response by performing an inverse Fourier Transform onthe result of the dividing step.
 46. The computer program of claim 37,wherein the determined step response is an average of a number ofacquired step responses derived from said signal.